The magnetic fields generated by spins and currents provide a unique window into the physics of correlatedelectron materials and devices. Proposed only a decade ago, magnetometry based on the electron spin of nitrogen-vacancy (NV) defects in diamond is emerging as a platform that is excellently suited for probing condensed matter systems: it can be operated from cryogenic temperatures to above room temperature, has a dynamic range spanning from DC to GHz, and allows sensor-sample distances as small as a few nanometres. As such, NV magnetometry provides access to static and dynamic magnetic and electronic phenomena with nanoscale spatial resolution. Pioneering work focused on proof-of-principle demonstrations of its nanoscale imaging resolution and magnetic field sensitivity. Now, experiments are starting to probe the correlatedelectron physics of magnets and superconductors and to explore the current distributions in low-dimensional materials. In this Review, we discuss the application of NV magnetometry to the exploration of condensed matter physics, focusing on its use to study static and dynamic magnetic textures, and static and dynamic current distributions.
Box 1| Measuring static fieldsHere we describe elementary considerations for the use of nitrogen-vacancy (NV) centres for imaging magnetic fields generated by static magnetic textures and current distributions.
Reconstructing a vector magnetic field by measuring a single field componentBecause the NV electron spin resonance splitting is first-order sensitive to the projection of the magnetic field B on the NV spin quantization axis, B||, this is the quantity typically measured in an NV magnetometry measurement 16 . It is therefore convenient to realize that the full vector field B can be reconstructed by measuring any of its components in a plane positioned at a distance d from the sample, where d is the NV-sample distance (provided this component is not parallel to the measurement plane). This results from the linear dependence of the components of B̂ in Fourier space 24,25 , which follows from the fact that B can be expressed as the gradient of a scalar magnetostatic potential. Moreover, by measuring B||(x, y; z = d) we can reconstruct B at all distances d + h through the evanescent-field analogue of Huygens' principle, a procedure known as upward propagation 24 . As an example, the out-of-plane stray field component Bz(x, y; z = d + h) can be reconstructed from B||(x, y; z = d) using ̂( ; + ℎ) = − ℎ̂| | ( ; ) NV •